Fundamentals of SIGLA,an interval computing system over the completed set of intervals

The SIGLA System has been designed to obtain an Interval Computing System working with the whole surrounding structure of the standard interval setI (R) (see 9]), that is, the lattice completion ofI (R) with the ordinary algebraic operations extended onto it. A statistical component associating intervals to Bounded Fuzzy Distributions is added. Rounding semantics onI ^* (R) is considered, and bounding theorems directing programming are given. Improper intervals are shown to mean “control-band-like variables”, in contrast to the classical “autonomous random variables” represented by proper intervals. An outline of the SIGLA language is given.